According to Wikipedia the State Secrets Privilege (SSP) is "an evidentiary rule - e.g., doctor-patient, lawyer-client or priest-penitent privilege - created by United States legal precedent. The court is asked to exclude evidence from a legal case based solely on an affidavit submitted by the government stating court proceedings might disclose sensitive information which might endanger national security." It also says its origin is based in English common law. In theory it sounds like a great idea. In practice it hasn't worked out so well. Kevin Poulsen put it best when he wrote that cases where it's been invoked seem "a pantheon of injustice". There are lots of scattered cases of it through the last thirty years or so but under George W Bush we've had a quick succession of them to give us the chance to focus on it.
The first argument against it is that it isn't even a law. In an example of judicial activism the usual suspects don't get too excited about the Supreme Court decreed it into existence in U.S. v Reynolds. It's a judicial precedent based on custom and if you really want to be a strict constructionist you should consider the ruling an outrageous infringement on the legislature's prerogatives. If state secrets are so urgent and precious let the House and the Senate pass a law concerning them and have the President sign it. What is so provocative about that? As it stands I think the courts have latitude to interpret the law and respect traditions and precedents (though not be bound by them). There are, however, a lot of people who start hyperventilating when the court does something interpreted as legislating from the bench. Those folks should be expected to oppose the SSP on fundamental belief.
I believe there's a much more compelling argument against it, and that is the importance of transparency. We ought to believe that government is obligated to disclose what it is up to. In fact, we ought to be substantially biased in favor of it. Looking at Poulsen's examples gives you all the idea you need about what happens when government is allowed to claim national security in order to prevent disclosure: It uses the claim to cover up embarrassing or incriminating details. In none of the examples is there an actual national interest at stake. We should proceed on the assumption that that is always the case and dispose of the whole thing. In the extremely rare cases where national security is at stake there will probably be other, more compelling issues that would allow the protection of the secrets. And in the positively microscopic percentage of cases where even that wasn't true let me give you an analogy.
I'm in the jury box and Jack Bauer is in the dock. He Ramboed his way into Pakistan and caught Osama. Took him alive not dead because he's a professional and wouldn't even take bin Laden's life needlessly. On the way back to the plane his captive let slip that he knew about a nuclear bomb somewhere in Manhattan that would explode shortly. Jack tortures the answer out of him, notifies the government, experts are rushed to the scene, the bomb is defused and the day is saved. But torture is illegal because of those darn civil liberties types and now he has to stand trial. Know what? I vote him not guilty. I suspect every jury you could convene in this country would do so as well.
The SSP is the same in that the reasons given for it are as exceedingly rare as the "ticking time bomb" scenario used to justify torture. The problem is that as with torture the SSP will inevitably be abused once it is legal, and as with torture we should consider that price unacceptably high. It is a privilege that prevents us from knowing what our government is doing, and that veil of secrecy is a very appealing tool for cover-ups in the best of circumstances. In a time where the President has an authoritarian streak it will (big hat tip Marcy Wheeler) be invoked with alarming frequency.
The point is this: You state the principle and you live by it. And when the nearly unique exceptions pop up you trust that a well-informed citizenry will understand and make allowances as needed. We have almost no secrets that require an SSP. Overturn it. We'll be sensible about it if someone asserts it in a true national security emergency.